I moved from prep to state primary at the age of 9 and it was disastrous for me. I spent so many years repeating things I'd done at prep school (until I was about 13) that by the time it came to start paying attention I had become very lazy, and as a result didn't perform as well as I could have in my exams. It's only now, in my 30s, that I'm getting the work ethic back!
I was also bullied horribly for being a "snob" and "posh" because I'd been to fee paying school. It was an awful time.
I wouldn't do it to my children having had the experience I had, but appreciate that others may have had different outcomes - I'm just sharing one viewpoint.